Global Optimization Algorithm Based on Self- Organizing Centroids Sami Barmada, Marco Raugi, Mauro Tucci Dept. of Energy and Systems Engineering University of Pisa Pisa, Italy {mauro.tucci; marco.raugi; barmada}@dsea.unipi.it Abstract—This paper presents a stochastic real-parameter optimization algorithm which is based on the paradigm of the self-organizing maps (SOM) and competitive neural networks. The proposed algorithm is population based and a mutation and a selection operators are defined in analogy to standard evolutionary algorithms (EAs). In the proposed scheme the individuals move in the search space following the dynamics of a modified version of the SOM, which is based on a discrete dynamical filter. The proposed approach tries to take advantage of the explorative power of the SOM, and defines a new search strategy which is based on a combination of a local task and a global task, using neighborhood interactions. The proposed algorithm performance is compared with standard and state of the art variants of differential evolution (DE) algorithm. Wilcoxon tests show that the porposed algorithm is competitive with DE, advantages and disadvantages are outlined. Keywords-self-organizing maps; evolutionary algorithms; global optimization;differential evolution I. INTRODUCTION Global optimization is a recurrent task in a huge number of applications. Evolutionary algorithms (EAs) [1] are a family of population based stochastic search methods that allow performing very complex search and optimization. EAs are based on the imitation of the processes involved in the biological evolution and define a number of metaheuristics to exploit the underlying relation between optimization and biological evolution. The field of nature-inspired optimization algorithms is mostly constituted by the evolutionary algorithms and swarm intelligence algorithms, although the field also includes self-organizing systems, artificial life, memetic and cultural algorithms. Examples of EAs are genetic algorithms (GAs), evolutionary programming (EP), evolution strategies (ESs), genetic programming (GP), differential evolution (DE) and so on. Swarm intelligence algorithms include ant colony optimization (ACO), particle swarm optimization (PSO), bees algorithm, bacterial foraging optimization (BFO), etc. Among EAs differential evolution (DE) [2]-[5] is possibly acclaimed as one of the most powerful, and simple to implement, stochastic optimization algorithms existing. Particle swarm optimization is also very popular and easy to code, but it has been shown by many studies and comparisons that the performance of DE and its variants is largely better than the PSO variants over a wide variety of problems [11]. In this work a new stochastic real-parameter optimization algorithm is presented for global optimization, and we compare it directly with the DE algorithm. In the following we consider the minimization of an objective function, or fitness function   F x .   : D F    , x  , where  is a non-empty set serving as the domain of the search Some desired general requirements of such optimization algorithms are the following:  Simple and straightforward to implement.  Good performance in comparison with several others in a range of problems.  The number of control parameters should be low. The proposed algorithm is based on the paradigm of the self-organizing maps (SOM) and competitive neural networks. The self-organizing map [6] is a popular neural network for unsupervised learning, which has a wide number of applications from clustering to data visualization. In general the SOM has a strong explorative power, as it creates a vector quantization of the input distribution, where the centroids are disposed in a predefined topological order. It has been shown that the topology preserving factor of the SOM accelerates the vector quantization with respect to non topology preserving methods [12]. The proposed approach tries to take advantage of the explorative power of the SOM for optimization. A new heuristic strategy is defined, where each cell of the SOM contains a centroid, or an individual, which is an agent with a given personal task, and which is affected also by a global task through neighborhood interactions. In particular the local task of the centroid is to move in the search space and reach the personal target, which is the point with lowest fitness that has been generated as a perturbation of the centroid. The global task is to track the global target, which is the global best solution found by all centroids. The movement of the centroid of each cell is obtained as the output of a discrete filter, whose input is a combination of the local target and the global target. In this combination a neighborhood function has a role. Moreover the amount of the movement is regulated also by a goodness function, that indicates the relative goodness of the fitness of the personal target of each cell. In order to analyze and compare the proposed algorithm, we use the set of problems proposed for CEC competition on real-parameter optimization problems in 2005. This U.S. Government work not protected by U.S. copyright WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia IEEE CEC